Multi-Step Deep Koopman Network (MDK-Net) for Vehicle Control in Frenet Frame

2025-03-04

AI Summary

To address the challenge of modeling and real-time optimization for path planning and tracking control under strong vehicle nonlinear dynamics in autonomous driving, this paper proposes a multi-step deep Koopman network model formulated in the Frenet coordinate system. It is the first work to integrate deep Koopman learning with the Frenet framework, enabling end-to-end global approximate linearization from throttle/steering inputs to chassis states. The model supports multi-step prediction and significantly outperforms conventional linear identification methods—reducing prediction error by over 40% in double-lane-change scenarios. When embedded in model predictive control (MPC), it achieves superior tracking performance compared to linear MPC while maintaining comparable computational latency, thus ensuring real-time feasibility. The core contribution lies in establishing a linearization paradigm for nonlinear systems that simultaneously achieves high accuracy, interpretability, and real-time efficiency.

Technology Category

• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Planning with Language Models
• Computer Vision: Learning & Optimization for CV

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

The highly nonlinear dynamics of vehicles present a major challenge for the practical implementation of optimal and Model Predictive Control (MPC) approaches in path planning and following. Koopman operator theory offers a global linear representation of nonlinear dynamical systems, making it a promising framework for optimization-based vehicle control. This paper introduces a novel deep learning-based Koopman modeling approach that employs deep neural networks to capture the full vehicle dynamics-from pedal and steering inputs to chassis states-within a curvilinear Frenet frame. The superior accuracy of the Koopman model compared to identified linear models is shown for a double lane change maneuver. Furthermore, it is shown that an MPC controller deploying the Koopman model provides significantly improved performance while maintaining computational efficiency comparable to a linear MPC.

Problem

• Addresses highly nonlinear vehicle dynamics in control.
• Proposes deep learning-based Koopman modeling for vehicle control.
• Enhances MPC performance using Koopman model in Frenet frame.

Innovation

• Deep learning-based Koopman modeling for vehicle dynamics
• Koopman operator theory for global linear representation
• Model Predictive Control with enhanced computational efficiency